78 



THE STUDY OF SPEECH CURVES. 



Fig. 73. — Irregular curve. 



periods T, \T, [T, ^T, \T, IT, and the amplitudes 10, 5, 5, 5, 5, 5 

 (actual plot in figure 78) gives the results shown in the harmonic plot in 

 figure 79. It might be thought that, even if the composition of a curve 

 is unknown, the presence of the inharmonic would indicate itself in the plot 

 in figure 79, but there is nothing to distinguish it — or the original curve — 

 from a curve with the first five harmonics and the ampUtudes 12, 7.7, 11.9, 



10.9, 6.8, for which both the actual and the har- 

 monic plots would coincide with the plot 

 in figure 79. In the case of a curve 

 composed of simple sinusoids with the 

 periods T, \T, \T, LT, \T, \T, and the 

 ampUtudes 10, 5, 2, 2, 3, 5 (actual plot 

 in figure 80), the harmonic analysis (plot 

 in figure 81) does not furnish even a hint 

 that an inharmonic is present. 



We can thus draw 



I , the conclusion that, al- 



though the harmonic 



analysis represents the 



way in which the curve 



may have been produced, it does not of itself give 



the actual way except in cases where only harmonic 



elements were used for the composition. 



Since any periodic curve can be represented by a 

 harmonic series of simple sinusoids, the analysis can be 

 applied to speech curves. Is such an analysis any- 

 thing more than a mathematical performance? Even 



70 



60 



40 



30 



20 



10 



Fio. 75.— Sinusoid with 3i 

 waves to fundamental. 



70 



I 2 3 4 5 6 7 8 e 10 II 12 



Fio. 74. — Harmonic plot to fig. 73. 



60 



50 



40 



30 



20 



(0 



ii 



I I I 



I 2 3 4 5 6 7 8 9 10 II 12 13 14 13 15 17 IB 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 3536 



Fig. 76.— Harmonic plot to figure 75. 



if it is nothing more, has it a value for the study of speech curves? To 

 be anything more than a purely mathematical operation, the analysis 

 must represent the way in which the vowel vibration is produced or 

 perceived. If the vowel was actually produced by combining simple 

 sinusoid vibrations in a harmonic series, then this form of analysis gives 

 the elements directly. The sounds from the musical instruments are 

 presvmiably produced in this way, but we dare not assume that the vowels 

 are so produced until the fact has been proven. 



If we suppose an actual vowel curve to have been produced by the 

 addition of a number of harmonic and inharmonic sinusoids, we must 



